'Observables' in causal set cosmology

For the theories known as classical sequential growth (CSG) models, it has been conjectured that, up to sets of measure zero, the 'stem sets' generate the full σ-algebra of label-invariant measurable sets of causal sets. We prove this for a generic family of CSG models (the 'generalized percolation models'). In consequence, we are able not only to identify the 'observables' of these theories, but, more importantly, to provide them with an accessible physical interpretation. We suggest that the stem sets will play the same role of fundamental observable in the quantum analog of these theories, i.e. for quantum gravity